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Simplifying 3x2 + 42x = 150 Reorder the terms: 42x + 3x2 = 150 Solving 42x + 3x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 42x + 3x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 42x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-50 + 14x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-50 + 14x + x2)' equal to zero and attempt to solve: Simplifying -50 + 14x + x2 = 0 Solving -50 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 14x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 14x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 14x + x2 = 0 + 50 14x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 14x + x2 = 50 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 50 + 49 Reorder the terms: 49 + 14x + x2 = 50 + 49 Combine like terms: 50 + 49 = 99 49 + 14x + x2 = 99 Factor a perfect square on the left side: (x + 7)(x + 7) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + 7) equal to 9.949874371 and -9.949874371.Subproblem 1
x + 7 = 9.949874371 Simplifying x + 7 = 9.949874371 Reorder the terms: 7 + x = 9.949874371 Solving 7 + x = 9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 9.949874371 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.949874371 + -7 x = 9.949874371 + -7 Combine like terms: 9.949874371 + -7 = 2.949874371 x = 2.949874371 Simplifying x = 2.949874371Subproblem 2
x + 7 = -9.949874371 Simplifying x + 7 = -9.949874371 Reorder the terms: 7 + x = -9.949874371 Solving 7 + x = -9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -9.949874371 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.949874371 + -7 x = -9.949874371 + -7 Combine like terms: -9.949874371 + -7 = -16.949874371 x = -16.949874371 Simplifying x = -16.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.949874371, -16.949874371}Solution
x = {2.949874371, -16.949874371}
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